Question

Suppose x has a distribution with μ = 26 and σ = 25. (a) If a random sample of size n = 31 is drawn, find μx, σ x and P(26 ≤ x ≤ 28). (Round σx to two decimal places and the probability to four decimal places.) μx = σ x = P(26 ≤ x ≤ 28) = (b) If a random sample of size n = 59 is drawn, find μx, σ x and P(26 ≤ x ≤ 28). (Round σ x to two decimal places and the probability to four decimal places.) μx = σ x = P(26 ≤ x ≤ 28) =

Answer 1

Solution :

Given that,

mean = = 26

standard deviation = = 25

n = 31

= 26

= / n = 25 / 31 = 4.49

P(26 < < 28 )  

= P[(26 - 26) / 4.49 < ( - ) / < (28 - 26) / 4.49 )]

= P(0 < Z < 0.45 )

= P(Z < 0.45) - P(Z < 0)

Using z table,  

= 0.6736 - 0.5  

= 0.1736

n = 59

= 26

= / n = 25 / 59 = 3.25

P(26 < < 28 )  

= P[(26 - 26) / 3.25 < ( - ) / < (28 - 26) / 3.25 )]

= P(0 < Z < 0.62 )

= P(Z < 0.62) - P(Z < 0)

Using z table,  

= 0.7324 - 0.5  

= 0.2324